Tools and Techniques for Curves Tracing in Nineteenth Century Techno-Scientific Culture: Daniel Eichberg’s Ellipsograph Described by G.A. Breymann

Abstract The essay analyses the role of mathematical machines for the control of shapes in architecture between the eighteenth and nineteenth centuries through the link between knowledge of geometry, theoretical speculation and site practice. The investigation delves into D. Eichberg’s ellipsograph, an instrument capable of tracing both the ellipse and its normal, described in Breymann’s Trattato Generale di Costruzioni, Vallardi, Milano, (1885). Through the analysis of geometric principles and the creation of a prototype, the research verifies the correspondence between the graphical representations of the considered geometric properties and the operation of the instrument. Its utility in solving construction problems is highlighted, such as the tracing of joints, correct orientation of mortar beds and the division of an elliptical profile into ashlars, tasks that require knowledge of the normals to the curve. In conclusion, the contribution highlights that knowledge of these instruments is essential for reconstructing the history of geometry applied to the art of building and the techno-scientific debate among theoretical speculation, professional application, teaching, which are still relevant today.